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You can't use just hours and minutes as argument to the -t option. Usage is:

-t [[CC]YY]MMDDhhmm[.SS]

find will work

# assume 15 minutes ago
a=$( date +%H%M )
a=$(( $a - 15 ))
touch -t $a /tmp/dummy1
find /path -newer /tmp/dummy1 -exec ls -l {} \;

you can compute that value but it will...